Multi-objective optimization for the BTES system design

The multi-objective optimization (MOP) strategy starts from results of a previous energy, exergy and thermoeconomic analysis (Cosentino, et al., 2015; Cosentino, et al., November 13-19, 2015,). An energy and exergy parametric analysis has been proposed in order to investigate the optimal time required by BTES to charge the ground to the design temperature and to maintain the internal energy in the ground constant after each year (Cosentino, et al., 2015). The parametric study has been performed in different operating conditions as different installation depths and different distances between boreholes. The range of pitches is 3-7 m with a space step of 1 and the range of installation depths is 25-125 m with a space step of 25. The various combinations of pitch-depth selected for the analysis result in 25 different BTES configurations, each one with a proper length and a proper thermal extraction capacity. Results have shown that the optimal charging time significantly depends on the design parameters. It varies from 30 to 86 days for boreholes with pitch of 3 m at the installation depth gradually increasing. The optimal charging

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time reaches the value of 994 days for the design with deepest and furthest boreholes. A summer recharging time of about 20 days is necessary for all designs to guarantee constant internal energy in the soil between two equal operation seasons (Cosentino, et al., 2015). Figure 3.12 clarifies the concept of constant internal energy showing two different operating conditions for the same system in term of recharging time. The first operating condition (dashed blue line) is performed with a non-optimal recharge stage with a consequent internal energy U2

(at the end of the second year of operation) lower than U1. In the second operating

condition (red line), the optimal recharging time ensures an internal energy U’2

approximately equal to that of the previous year.

Figure 3.12: Average Ground Temperature with two different summer recharging time (Cosentino, et al., 2015).

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Energy and exergy efficiencies have been calculated considering 10 years and 20 years of operation. The exergy efficiency or second law efficiency has been evaluated according with the following equation:





where 𝐸𝑥_{𝐸𝑥𝑡,𝑖} is exergy extracted at each season of operation, 𝐸𝑥_𝐼,𝐶ℎ is the exergy associated to the first charge stage (needed to achieved the design temperature in the ground) and 𝐸𝑥_{𝑅𝑒𝑐ℎ,𝑖} is the exergy associated to each recharge stage (needed to maintain constant the internal energy in the ground between two consecutive seasons of operation).

For each design both efficiencies increase with increasing operation time. This means that the amount of energetic (or exergergetic) resource stored in the charge stage is used and so exploited during the operation. A system with shallow and near boreholes is characterized by an efficiency of about 36% after 10 years and about 40% after 20 years of operation. These values decrease with increasing depth and pitch up to about 15% after 20 operation years (Cosentino, et al., 2015). These results allow to conclude that BTES plants with small size result more advantage in term of charging time and efficiency, especially for a long period of plant operation. The efficiency value for long operation period and the relative charging time can be considered two new indicators to take into account for selecting the type of plant during the design. The logic to maintain the internal energy in the ground constant during the years of operation can also represented a tool of optimization that maximizes the efficiency.

This approach needs to be combined with an economic analysis. Installation costs depend on the number of perforations more than depth. From an economic point of view, this would lead to prefer a reduced number of boreholes but deeper

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contrasting the parametric analysis results. In addition, installation of boreholes at large depth and small pitch is technically difficult to perform, with high risk of drill crossing (Cosentino, et al., 2015).

For these reasons, the thermoeconomic analysis has been developed in (Cosentino, et al., November 13-19, 2015,) for the selections of BTES configuration. Boreholes are designed to charge the ground to the design temperature and to supply heat to an underfloor heating system directly connected with the users without any heat pump. The underfloor heating system provides a constant thermal power of 100 kW through water that flows in the BTES at 35°C until to achieve 38 °C. The same configurations of (Cosentino, et al., 2015) are explored but two possible levels of storage temperature (45°C and 55°C) are proposed in order to investigate about the influence of the ground temperature on the performance (Cosentino, et al., November 13-19, 2015,). The exergy analysis is needed to compare the two scenarios at different temperatures of operation. Also in this case, for each configuration the charging time is evaluated to ensure a constant internal energy of the ground during the operation and the first and second law efficiencies are calculated for 20 years of operation. The efficiency is resulted higher for installation in reduced volume of the ground. Furthermore the efficiencies have proved to be greater in the case of storage and installation of the plant in the ground at higher temperature (55°C) (Cosentino, et al., November 13-19, 2015,). The trend of unit exergetic costs has confirmed the results obtained by the energy and exergy analysis i.e the most efficient configurations are characterized by the lower value of the exergetic cost. The unit exergoeconomic cost is resulted high for the most performance configurations and it seems to be particularly influenced by the unit exergoeconomic cost of the resource (Cosentino, et al., November 13-19, 2015,). Although storing energy in larger ground volume needs a reduced number of boreholes, the increase of the exergetic resource that follows, influences so the unit

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cost as causes its increase. The unit exergoeconomic cost has turned out to be lower in the case of storage at high temperature. This last result suggests that a better exploitation of the energy stored in the charge stage occurs when the storage is at higher temperature. Although the storage at higher temperature involves longer charging time and higher initial costs, these are amortized in the years of operation (Cosentino, et al., November 13-19, 2015,).

The proposed methodology for the design of BTES system has been presented at ASME 2015 conference and it has been awarded with the prestigious ASME

Edward F. Obert Award.

The MOP considers the results presented in (Cosentino, et al., November 13-19, 2015,) to define the competing objectives, the decision variables and the relative constrains. The unit exergoeconomic cost cp and the exergetic efficiency 𝜀_𝐼𝐼 are

selected as function to optimize. The productive structures in term of resources and products are explained in detail in (Cosentino, et al., November 13-19, 2015,). The decision variables are the design parameters i.e. the pitch p and the installation depth 𝐿𝑑. The MOP problem can be summarized as follows:

𝑚𝑖𝑛(𝑭(𝑝, 𝐿_𝑑)) = min (𝒄𝒑(𝑝, 𝐿𝑑), −𝜺𝑰𝑰(𝑝, 𝐿𝑑)) (3.16)

subject to { 3𝑚 ≤ 𝑝 ≤ 6𝑚 100𝑚 ≤ 𝐿𝑑≤ 125𝑚

The multi-objective genetic algorithm function gamultiobj of Matlab tool has been used to solve Eq. (3.16).

For each possible design solution (p, Ld) the population given by Matlab function,

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are evaluated according with a complex procedure which schematic representation is reported by Figure 3.13.

Figure 3.13: Multi-objective strategy with POD modelling.

Each design point (p and Ld) is characterized by a proper heating extraction capacity

and by the corresponding number of boreholes. In order to evaluate them, an iterative process (block B) has been proposed, as illustrated in Figure 3.14.

The design condition corresponds to minimum external temperature in the winter season, during which the thermal power is required for 18 hours. For a possible plant located in Turin, the minimum design temperature is -8°C and the indoor design temperature is 20°C.

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Figure 3.14: Iterative process to the thermal power calculation in the design condition.

Assuming that the design condition occurs exactly at mid-season, the heating extraction capacity Φ_𝑑𝑒𝑠can be calculated using the degree-day theory (Cosentino, et al., November 13-19, 2015,) and compared with the heating extraction capacity Φ_{𝑑𝑒𝑠,𝑠𝑖𝑚} given by the POD model.

The output of the procedure B is the input for simulating the operation (block C) with the reduced model (see Figure 3.15). The energy analysis downstream the discharge stage allows establishing if the configuration is suitable for providing the daily energy in the winter season. The energy demand is calculated according with

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the average daily outside temperature. A configuration is unsuitable if it requires more than 24 h to satisfy the heating requirement of one day.

Figure 3.15: Verification and simulation of BTES operation with POD model.

For the suitable configurations, the charging time for bringing the design ground temperature and the relative amount of energy and exergy storage in that period, are evaluated. A constant internal energy between two consecutive seasons of

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operation can be guaranteed thanks to a recharging stage at the end of the winter season. The recharge is obtained using the district heating network. The evaluation of recharging time and relative energy and exergy stored are performed considering that the two consecutive heating seasons are the same.

For each configuration, the second-law efficiency and the unit exergoeconomic cost are evaluated considering 20 operation years, under the hypothesis that the winter seasons repeat themselves without changing.

Figure 3.16: Pareto front of MOGA optimization for the BTES system.

The Pareto front of the MOP strategy is reported in Figure 3.16. The Pareto front is the objective space where the values of objective functions related to each optimal solution are plotted. A solution is Pareto-optimal if it is not dominated by any other

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solution in decision variable space and the set of all these solutions is called the Pareto-optimal or non-dominated set.

The unit exergoeconomic cost increases moderately of about 52.2% as the exergecit efficiency increases of about 38.6%. As shown in Figure 3.16, the maximum exergetic efficiency exists at design point C (18.2%), which the greatest exergoeconomic cost corresponds (0.064 €/kJ). On the other hand, the minimum value for the cp occurs at design point A which is about 0.031 €/kJ. Design point A is the optimal situation when the unit exergoeconomic cost is the only objective function, while design point C is the optimum point when exergetic efficiency is the only objective function. In multi-objective optimization, a process of decision- making for selection of the final optimal solution from the available solutions is required. The process of decision-making is usually performed with the aid of a hypothetical point in Figure 3.16(the ideal point), at which both objectives have their optimal values independent of the other objectives. The ideal point is not a solution located on the Pareto frontier because it is impossible to have both objectives at their optimum point simultaneously, as shown in Figure 3.16. The closest point of the Pareto frontier to the ideal point might be considered as a desirable final solution.

Note that in multi-objective optimization and the Pareto solution, each point is a optimized point. Therefore, the selection of the optimum solution depends on the preferences and criteria of the decision maker, suggesting that each may select a different point as for the optimum solution depending on the needs. A good trade off in term of efficiency and cost could be given by the design point B for which

p=3 m and Ld = 120 m and the correspondent efficiency and unitexergoeconomic cost are 16% and 0.048 €/kJ respectively.

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